If the same search is carried out across different search engines, it is likely that you will see different results says Robert of www.bobsseo.com in Las Vegas, Nevada. The reasons for this are because each search engine uses a proprietary algorithm which applies different weighting factors to determine what results show up in their result pages when a search query is entered.
Since Google is the dominant search engine across the globe it makes sense to focus your efforts on them. An authority site that ranks well in Google generally tends to rank well in Yahoo and Bing too. This is because most of the important factors relating to On Page and Off Page SEO will already have been adhered to if your website ranks well in Google. Another way of looking at this is to view Google as the quality control.
Depending on which country you are based in, the traffic that flows through Google is typically anything between 64-90% of all search engine queries.